A number is multiplied by 5, and then the product is added to 23. the result is 53. what is the number?

Derek's design is a kite which starts with coordinates: A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to th

katrin [286]

Answer:

The answer is below

Step-by-step explanation:

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Solution:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

If a point X(x, y) is translated b units up and a units right, the new point is X'(x + a, y + b). If a point X(x, y) is translated b units down and a units left, the new point is X'(x - a, y - b)

If X(x, y) is reflected across the y axis, the new point is X'(-x, y)

If X(x, y) is reflected across the x axis, the new point is X'(x, -y)

If X(x, y) is rotated 180 degrees, the new point is X'(-x, -y)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to the left and 3 units down the new point is A'(-3, -3), B'(-1, -5), C'(-3, -8), D'(-5, -5). If it is then reflected across the y axis, the new point is A"(3, -3), B"(1, -5), C"(3, -8), D"(5, -5).

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he reflected across the x-axis the new point is A'(2,0), B'(4, 2), C'(2, 5), D'(0, 2). If it is then rotated 180 degrees, the new point is A"(-2, 0), B"(-4, -2), C"(-2, -5), D"(0, -2). If it is translated 1 unit left the point would be A"'(-3, 0), B"'(-5, -2), C"'(-3, -5), D"'(-1, -2)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he rotated 180 degrees the new point is A'(-2, 0), B'(-4, 2), C'(-2, 5), D'(0, 2). If it is then translated it 3 units up and 1 units left, the new point is A"(-3, 3), B"(-5, 5), C"(-3, 8), D"(-1, 5).

8 0

3 years ago

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100μ=100 and a standard deviation sigma

Ksivusya [100]

Answer:

51.60% probability that a randomly selected adult has an IQ between 86 and 114.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 114, \sigma = 86$

Find the probability that a randomly selected adult has an IQ between 86 and 114.

Pvalue of Z when X = 114 subtracted by the pvalue of Z when X = 86. So

X = 114

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{114 - 100}{20}$

$Z = 0.7$

$Z = 0.7$ has a pvalue of 0.7580

X = 86

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{86 - 100}{20}$

$Z = -0.7$

$Z = -0.7$ has a pvalue of 0.2420

0.7580 - 0.2420 = 0.5160

51.60% probability that a randomly selected adult has an IQ between 86 and 114.

3 0

4 years ago

6. (5 points) Graph using two intercepts; show your work in finding the intercepts. 6x - 3y = 18

Setler [38]

Answer:

Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:

$6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1$ The two intercepts are then 3 and -6.

(I know, dividing by 3 both sides of the equations would have made the whole process way easier).

Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.